Stability Properties of the Different Types of Equilibria

Abstract

In this chapter some stability properties of equilibria of the models from the preceding section will be investigated. The system

$$ \left\{ {\matrix{ {\mathop m\limits^ \circ = M(m,w,y)} \hfill & {(m,w,y)' \in X} \hfill \cr {\mathop w\limits^\circ = W(m,w,y)} \hfill & {} \hfill \cr {\mathop y\limits^ \circ = Y(m,w,y)} \hfill & {} \hfill \cr } } \right. $$

(4.20)

has several types of equilibria. As already pointed out in Section 4.5, for any element of the sets C and u the inequality$\mathop w\limits^ \circ \ne 0$ holds. So, equilibria of system (4.20) within these sets are impossible. There may be equilibria in the sets cl K and cl I. Equilibria in the sets K and I will be called Keynesian and Inflation equilibria, respectively. In an Inflation equilibrium the price of the good, the nominal wage rate w_n and the nominal money stocks m_n grow at the same rate. This inflation, however, does not affect the traded quantities of labour ℓ̂ and goods r̂, that are constant over time. In a Keynesian equilibrium the variables p, w_n and m_n decrease proportionally, so that there is a constant deflation and the quantities ℓ̂and r̂ are constant again.